1. Environmental Economics 2
The Travel Cost Model
Prof. Anil Markandya
Department of Economics and International Development University of Bath
Environmental Economics 2
February,

2. The Travel Cost Model (TCM)
The typical problem of the travel cost model
Basic assumptions
weak complementarity
The single site model
Poisson, Negative Binomial
The problem of on-site sampling
Example with Limdep
The multi-site model
Conditional logit model
Independence of Irrelevant alternatives

3. The demand for recreation
Objective: how revealed preference data can be used to estimate welfare changes caused by different public programs:
- change in the quality of a characteristic of a recreational area (example: decrease in the level of pollution of the water at a beach)
- Closure of the site (the access to the beach is forbidden)
The TCM is based on REVEALED PREFERENCES

4. The origin of the TCM
Harold Hotelling (1949) “An Economic Study of the Monetary Valuation of Recreation in the National Parks,” Washington, DC: U.S. Department of the Interior, National Park Service and Recreational Planning Division.
In a letter to the US Park Service, Hotelling suggests to use TCM to assess the benefits obtained by visitors of a national park.
Intuition behind the TCM:
Need to travel to reach a site in order to enjoy it
When I decide to visit a site I need to pay a cost to reach (and enter) the site
The cost to reach (and enter) the site and the number of visits to the site allow me to estimate a lower bound of the value of the site
I estimate only use-values (non-use values can be assessed through the Contingent Valuation Method)

5. Basic assumptions
The cost of the travel and of the time spent to reach and stay at the site are a proxi for the value of the recreational experience
Use value is assessed taking into account the number of homogeneous visits to the sites among respondents
Homogeneous => visits last same amount of time; I don’t want to mix 1 day visits with multi-day visits!
Visits to only one site; avoid visitors that in one day visit several sites (site A, site B, site C…)
=> problem to assess the welfare obtained from site A, from site B and so on

6. Weak complementarity
I assume that the environmental quality of the site affects the number of visits to the site.
I assume that if the number of visits is 0, it remains 0 even if there is a marginal increase in the quality of the site.
The weak complementarity assumption allows us to identify how the variation in a public good affects the behaviour of a person.
The idea behind the weak complementarity assumption is to link a private and a public good so that if the private good is not consumed, I cannot estimate the public good.
The basic idea behind the indirect methods of environmental valuation is to infer the monetary value of a change in the level of environmental services of interest from observed market data on some ordinary commodity.

7. The single site model
The single site model describes the demand for recreation of a person during a season (12 months)
The quantity demanded is the number of visits
The price is the cost per visit
r = number of visits during a season
tcr = cost of a visit
Intuition: who lives close to the site has a low cost per visit. He should visit the site more often than someone who lives further away.

8. What determines the number of visits
In equation (1) we assumed that only the cost affects the number of visits. Other elements, such as age of the respondent, income, experience, availability of substitute sites may affects the number of visits: 2.
tcs = price of trip to substitute site s (I expect a positive sign)
y = income
z = vector of socio-demographic characteristics of the respondent (age,experience, etc.) 3.
B = total trip cost
A+B = Willingness to pay
A = consumer surplus
A = Access value
The ‘choke price’ is the minimum price
at which the number of trips falls to zero.
The consumer surplus is equal to: 4.
‘choke price’
tcr A
tcr0 B r r0

9. Steps in estimating a single site model
Define the site to be valued
Define the recreation uses and seasons
Develop a sampling strategy
Specify the model
Decide on the treatment of multiple purpose trips
Design and implement the survey
Measure trip cost
Estimate the model
Calculate access value

10. Define the site to be valued
Single site model
What do we mean by “single site”?
A river
A lake
A beach
A park

11. Define the recreation uses and seasons
What are the site’s functions? Only one function? Or several functions (beach: fishing, swimming, sailing, etc.)?
Ask respondents what is their PRIMARILY purpose to visit the site
If recreation types are similar we can aggregate observations, otherwise we cannot.
when you present your results, motivate why you aggregated data from different recreation types
It can be useful to use dummy variables to take into account different recreation types
Decide the length of the season for recreation (summer, 12 months?)
Decide carefully when to do the interviews

12. Develop a sampling strategy
On-site sampling Vs off-site sampling
On-site sampling
- minimize costs
- fast collection of data
- ‘choke price’ not identified
- it is difficult that respondents remain focused on the interview => keep the questionnaire short
- who shall I interview? (a person every 5…) }
- the sampling plan is not representative of the population
- those who visit the site more often are more likely to be surveyed
Econometric problems

13. Off-site sampling (mail, telephone)
- I survey both visitors and non visitors
=> representative of the population
- ‘choke price’ is identified
- expensive: difficult to intercept users
- need to define the area to sample
=> maximum day’s drive to reach the site
- if you have a registry of users, then use it
=> registry of anglers, hunters, etc.

14. Specify the model
Identify the variables you want to use in your model:
-age, income, experience with the site and similar sites, leisure, job, education, equipment, starting point, length of the visit, number of visits, etc.
- don’t ask too many questions
- if on-site, no need of warm-up questions
- run focus groups, talk to people at the site, to users
- test the questionnaire

15. Decide on the treatment of multiple purpose trips
Goal: you want to survey daily users whose aim is to visit the site
If you are interviewing a person that does visit the site, but whose primary goal is not visiting the site (for example, visiting a friend) then you should delete this observation from the analysis

16. Design and implement the survey
The questionnaire is composed by 4 parts:
- introduction
- questions on visits to the site (and other substitute sites)
- questions on last visit (cost, number of people travelling with, starting point, arrival, length, goal of the visit, etc.)
- socio-demographic characteristics of the respondent
When to survey respondents? Not only on Saturdays and Sundays!

17. Measure trip cost - travel cost (return cost) - access fee
- equipment cost
- cost of time

18. Cost of time
The models to study the demand for recreation are models that study the allocation of time, therefore they are very sensitive on the assumptions on the value of time
Simple models assume it is possible to trade off leisure and work time. However, most people do not have the flexibility to shift time in and out of work in exchange for leisure.

19. Solution to the problem of time
n = respondent
rn = number of trips person n takes to the site
tcn = travel cost and entrance fee
wn = net wage per hour
tn = time person n spends at the site 1)
= 0 for a respondent that must work a fixed number of hours and cannot trade off leisure with work time;
= 1 for a respondent that can decide how many hours to work
=> It is important to ask respondents what type of job they have

20. Estimate the model
Count models for the demand for recreation (Poisson, negative binomial)
- Count models only consider non negative values of the dependent variable
The classic count model is:

21. The Poisson model The pdf of the Poisson is: 5.
is both the mean and the variance of the distribution. It is the expected value of visits. It is assumed to be explained by the independent variables in the model (age, income, etc.)
A log-linear form is useful in order to avoid negative probabilities: 6.
Parameters in equation (6) are estimated by maximum likelihood: 7.
Consumer surplus, or access value, for each person in the sample is: 8.
is the expected number of trips for person n from equation 6

22. The negative binomial
The Poisson constrains mean and variance of r be identical: E(rn|znβ)=V(rn|znβ)=λn
Usually, in the studies of demand for recreation, the variance is larger than the mean, suggesting overdispersion of the data. As a consequence, the standard error estimated by the Poisson are underestimated => inefficient coefficients
The negative binomial is an approach for relaxing this constraint (we consider a version of the negative binomial model that is equal to a Poisson model with a gamma distributed error term in the mean):
Suppose the conditional mean from a Poisson model is the sum of znβ and an unobserved error term θn that represents unobserved individual preferences or unobserved heterogeneity:
E(rn)=exp(znβ+θn)
We assume that exp(θn)=vn has a normalized gamma distribution

23. The negative binomial model:
A test of α=0 is a test of H0 = Poisson model is the correct model
If you find α>0 then overdispersion exists and the correct model is the negative binomial. Also if α<0 the negative binomial is the correct model. LIMDEP does the test in automatic
The mean of the negative binomial is:
The variance of the negative binomial is:

24. On-site sampling
On-site random samples are truncated at one trip and oversample more frequent users => estimates from eq. 6 are biased
Solution: Endogenous stratified and truncated Poisson
In the Poisson model the dependent variable is (r-1), rather than r.
For the negative binomial model, the correction is more complicated and you need to program into Limdep the maximum likelihood routine:

25. Calculate access value
In the Poisson model, the access value is given by assessing Sn from eq. 8. The estimate of the access value for person n is given by:
If one has estimated a Poisson model using a randomly drawn off-site sample, an estimate of aggregate access value is:
where POPoff=total number of people in the relevant geographic market
N=number of surveyed persons

26. If one estimates a model with an on-site sample, the aggregate access value is given by:
POPon=total number of users in a season => somehow you need to find this number
nj=number of persons in the sample taking j trips to the site
R=largest number of trips taken by a person in the sample

27. The multi-site model
The multi-site model is not based on a “quantity demanded approach”, and describes the demand for recreation as a problem of choice among alternatives.
The model used is the random utility model (RUM).
Choices are explained by the characteristics of the sites.
We assume that respondents choose the sites that give them the highest level of utility.
This model allows to analyze the behaviour of economic agents when they are facing a problem of choosing which site to visit even when the alternative sites are many (even 1,000!)

28. Estimate of the multi-site model
Identify what we want to valuate
Define the population to sample
Define the choice set
Decide the sampling plan (on-site sampling is very troublesome)
Specify the model
Obtain information about the sites
Analysis of multi-objective visits
Data collection: I need to get information on all sites
Estimate of the cost per visit (to all sites)
Model estimates
Access value estimate

29. The random utility model
On a given choice occasion, a person considers visiting one of C sites denoted as i=1,2,3,….,C.
Each site is assumed to give the person a site utility vi.
Utilities are assumed to be a function of the trip cost and site characteristics
The utility for site i assuming a linear form is:
19.
tc = trip cost of reaching site i
qi is a vector of characteristics of site i
ei is a random error term
Site k is chosen if:
20.

30. An individual’s utility is:
U = max(v0, v1, v2, v3,…,vc)
V0 is the level of utility obtained by not visiting any site.
To capture differences in participation, respondents’ characteristics are captured as explanatory variables in the no-trip utility function:
v0 = α0+α1z+ei
z is a vector of characteristics believed to influence a person’s propensity for recreation
To capture differences in preferences for different sites, individual characteristics must be interacted with site characteristics.

31. Estimate the model The probability that a person visits site k:
Pr(βtctck+ βqqk+ek≥ βtctci+ βqqi+ei for all i є C and ≥ α0+α1z+e0 )
If the error terms are IID and follow a type I extreme value distribution, equation (37) is estimated through the conditional logit model:
38.
Parameters α and β are estimated by maximum likelihood:
39.
where pr(i) is the logit form from eq (38)
rin=1 if individual n visited site i, and =0 otherwise
In circumstances where individuals are observed taking multiple trips to
sites over the season, the same likelihood function is used, with rin now
equal to the number of trips taken to site i by individual n

32. The restriction of Indipendence of Irrelevant Alternatives (IIA)
This restriction implies that the relative odds of choosing between any two alternatives is independent of changes that may aoccur in other alternatives in the choice set.
Model (38) violates the IIA restriction.
The Nested Logit model and the Mixed Logit model (or Random Coefficient Logit model, or Random Parameter Logit model) by introducing correlation among the site and no-trip utility error terms allow for more general patterns of substitution in the model and tehrefore relax the IIA restriction.

33. Estimate Access Value
Suppose site 1 is closed. I estimate the welfare loss for person n from the closure of site 1 per choice occasion:
the negative of the coefficient on trip cost, is a measure of the marginal utility of income
If person n did not visit site 1 when it was available, then the welfare loss is equal to zero
Now suppose sites 1 through 5 are closed. I estimate the welfare loss for person n from the closure of sites 1 to 5 per choice occasion:

34. Estimate the value of a quality change
For a quality change the per choice occasion value for person n is:
where q*i is a vector indicating a quality change at some or all of the C
sites
The seasonal value for each individual is the total number of choice
occasions times the person’s per choice occasion value. The mean
seasonal per person value is:
=sample mean per choice occasion value
T=total number of choice occasions in the season (number of days in the
season)

35. The aggregate seasonal value over the population is:
where POP is the population of users and potential users

36. Fort Phoenix - New Bedford Beach
Off site
Telephone interviews
Visits to Fort Phoenix beach, New Bedford, in 1986.
N=499 interviews

37. Number of visits (r) to Fort Phoenix beach in 1986
Cumulative Cumulative
r Frequency Percent Frequency Percent

38. Descriptive statistics
x Trips to Fort Phoenix Beach in 1986 (in New Bedford, MA)
BEACH if respondent visited any beach in the last year, =2 otherwise
pfp if household has a pass tp Fort Phoenix, =0 otherwise
RES if the respondent resides in the Greater New Bedford area
AGE Age of the respondent
INC Household income in $10,000 units
c Round-trip travel costs plus monetary value of time to nearest substitute beach
cfp Round-trip travel costs plus monetary value of time to Fort Phoenix Beach
c Round-trip travel costs plus monetary value of time to next nearest substitute beach

40. WTP for visiting Fort Phoenix
From the Poisson model, the welfare that the average person receives from visiting Fort Phoenix are given by:
WTP = 3.83/0.47 = $8.15
3.83 = average number of visits to Fort Phoenix
0.47 is the negative of the coefficient of the cost to visit Fort Phoenix
Using the negative binomial:
WTP = 3.83/0.53 = $7.22